Simple Harmonic Motion

gravitational field

mass

amplitude

spring stiffness or constant

Cannot be determined

Sometimes

true

false

Immediately after release from rest at highest swing point.

Midway between high points during swinging motion.

At its lowest point during swinging motion.

At its highest point during swinging motion.

Total mechanical energy remains constant throughout the motion

The kinetic energy increases and decreases but does not remain the same

Potential energy varies but is not conserved over time

Only the potential energy due to gravity is conserved

$T = 2\pi \sqrt{\frac{M}{K}}$

$T = 2\pi \sqrt{\frac{L}{G}}$

$T = \pi \sqrt{\frac{M}{K}}$

$T = \pi \sqrt{\frac{L}{G}}$

Acceleration (a)

Amplitude (A)

Force (F)

Velocity (v)

It continuously increases as motion proceeds

It periodically changes between zero and maximum value depending upon object's velocity

It gradually decreases over time due to frictional forces acting on the system

It remains constant

It slowly diminishes over time due external forces acting upon system causing dissipation.

It alternates between different values but average value over one complete cycle isn't same every subsequent cycle thereafter.

Increasing steadily since there external force inputting more work each cycle.

Total mechanical energy remains constant throughout oscillation because there are no non-conservative forces doing work on or by system.

$T = \frac{1}{2\pi} \sqrt{\frac{L}{g}}$

$T = 2\pi \sqrt{\frac{L}{g}}$

$T = \frac{2\pi}{\sqrt{gL}}$

$T = 2\pi \sqrt{\frac{g}{L}}$

Frequency triples.

Frequency decreases by a factor of $\sqrt{3}$.

Frequency remains constant.

Frequency decreases by a factor of 9.